Behold! The most deliciously pedantic math argument in history! Person A thinks "1+1=2" is an equation (technically correct in everyday speak), while Person B is having a mathematical meltdown because it's ACTUALLY an identity (also technically correct in formal mathematics).
This is the mathematical equivalent of arguing whether a tomato is a fruit or vegetable. Both mathematicians are right in their own nerdy universes! In math-speak, an equation typically has variables to solve for, while an identity is always true regardless.
I bet these two also fight about whether 0.999... equals 1. *twirls calculator maniacally* THE HORROR!